Square-root regret bounds for continuous-time episodic Markov decision processes

TL;DR

This paper introduces a reinforcement learning algorithm for continuous-time episodic Markov decision processes, providing square-root regret bounds and demonstrating effectiveness through simulations.

Contribution

It develops a novel learning algorithm for continuous-time MDPs with theoretical regret bounds and empirical validation, extending RL theory beyond discrete-time models.

Findings

Regret bounds are of order square-root in the number of episodes.

The proposed algorithm outperforms baseline methods in simulations.

Both upper and lower bounds on regret are established.

Abstract

We study reinforcement learning for continuous-time Markov decision processes (MDPs) in the finite-horizon episodic setting. In contrast to discrete-time MDPs, the inter-transition times of a continuous-time MDP are exponentially distributed with rate parameters depending on the state--action pair at each transition. We present a learning algorithm based on the methods of value iteration and upper confidence bound. We derive an upper bound on the worst-case expected regret for the proposed algorithm, and establish a worst-case lower bound, both bounds are of the order of square-root on the number of episodes. Finally, we conduct simulation experiments to illustrate the performance of our algorithm.